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Abstract
Let 𝔄 be a finite abelian group. In this article, we classify harmonic 𝔄covers of a tropical curve Γ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on Γ. We give a realizability criterion for harmonic 𝔄covers by patching local monodromy data in an extended homology group on Γ. As an explicit example, we work out the case 𝔄=ℤ/pℤ and explain how realizability for such covers is related to the nowherezero flow problem from graph theory.
Original language  English 

Number of pages  22 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  FirstView 
Early online date  10 Oct 2023 
DOIs  
Publication status  Epub ahead of print  10 Oct 2023 
Keywords
 Coverings
 Fundamental group
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Dive into the research topics of 'Abelian tropical covers'. Together they form a unique fingerprint.Projects
 1 Active

Tropical Geometry and the moduli space o: Tropical Geometry and the moduli space of Prym varieties
1/05/23 → 31/10/25
Project: Standard